We study the proximity coherence in a mesoscopic normal-metal film in contact with a superconductor. Accounting for a repulsive interaction between the electrons in the normal metal, we find an enhanced local density of states close to the normal-metal superconductor interface. The sharp peak in the density is pinned to the Fermi energy and leads to spontaneous paramagnetic interface currents. The induced orbital magnetic moments exhibit the characteristic features of the paramagnetic reentrance observed in normal-metal coated superconducting cylinders [P. Visiani, A.C. Mota, and A. Pollini, Phys. Rev. Lett. 65, 1514 (1990)].